Optimal and heuristic search for a hidden object in one dimension

A common problem in computer science and applied engineering is to minimize the average cost of finding an object hidden at one of n possible locations embedded in a line or string. Among problems with this structure, one that has been well studied is “alphabet” or “left-right” search (LRS), in which each search reveals whether the object is to the left or to the right. If each location i has a known probability p_i of containing the object and a known cost c_i of search, then dynamic programming (DP) can be used to find an optimal adaptive search strategy for LRS in O(n³ ) time so that the expected cost is minimized. This paper introduces a generalization of LRS called interval search (IS), in which it costs an amount C_ij to determine whether the object lies between locations i and j. IS can also be solved by DP and can be approximately solved by a “maximum entropy reduction per unit cost” heuristic, as well as by a polynomial time restricted DP